To sum up, we see that at \(\tilde{m}^2\le 0\)  the infrared divergencies arise in the free energy. Therefore, a more accurate analysis of the low energy modes is required. These divergencies may be cured by introducing the Bose-Einstein condensate and summing the ring diagrams (see, e.g., [1]}, [2]}) or, as in the flat spacetime, by introducing the boundaries and accounting for the finite size effects. In the case, when
\(l\lesssim m^{-1}\ll L,\) 
